Since in this paper we will not be discussing anything specific to semi-algebraic graphs, we won't attempt to make Theorem REF  (and its connection to Theorem REF ) more precise by providing the required definitions, but we invite the interested reader to consult [1]}. Nevertheless, it is worth mentioning at least that this theorem has multiple applications in combinatorial geometry, as the case \(d_{1}=d_{2}=2\)  already directly implies the celebrated Szemeredi-Trotter theorem [2]}.
